Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #336 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,9,10,11)(13,15);(2,3)(4,5)(6,7)(12,13)(14,15)(16,17,18,20,19,21,22,23)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,c^2=f,b^a=be,g^a=g^6136 conjugacy classes — view the full character table.
| maximal subgroup of | #11725283, #11725284, #11725285, … |
| maximal normal subgroup of | #11725283, #11725284, #11725285, … |
| maximal quotient of | #11725417, #11725419, #11725420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 81);